So, men's rate is not even double womens'.
Don't get me wrong, both numbers are serious, and I agree it's a lot harder for us men. It's just that, particularly in the case of such an isolating feeling, excluding people and minimizing them is truly damaging.
There are plenty of things, such as unrealistic body image portrayed by the media, that affect both men and women, yet women claim it exclusively as theirs, because men aren’t supposed to. Can’t men have a thing?
This way of putting things, as if groups like "women" or "men" were clubs with decision making processes, is absurd and only serves to cause division and infighting.
I have literally been shut down in a conversation, in person, at work, more than once, because I was a white male in tech.
I don't see how your solution of "men hav[ing this] thing" helps men who have body image issues, nor women who don't feel they have close friends.
It's not like the dude with body image issues is saying "oh, thank god my problems would be recognized if only my issue were a lack of close friends."